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Given the collinear points A,B,C find the coordinates of C(2t,1-t) if A(3,3), B(2,4).

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sapon | Student, Undergraduate | eNoter

Posted April 27, 2011 at 1:35 AM via web

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Given the collinear points A,B,C find the coordinates of C(2t,1-t) if A(3,3), B(2,4).

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giorgiana1976 | College Teacher | Valedictorian

Posted April 27, 2011 at 1:40 AM (Answer #1)

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We'll use determinants to compute the coordinates of C.

We'll create the determinant of the coordinates of the given collinear points. The value of this determinant is zero if the points are collinear.

|3    3    1|

D =  |2    4    1|

|2t  (1-t) 1|

We'll calculate D:

D = 3*4*1 + 2(1-t)*1 + 2t*3*1 - 2t*4*1 - 3(1-t) -  2*3*1

D = 12 + 2 - 2t + 6t - 8t - 3 + 3t - 6

D = 5 - t

Since A,B,C are collinear => D = 0 <=> 5 - t = 0

t = 5

The coordinates of C are: C(10 , -4).

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